Hand-held electronic game machine



FIG. 1 is a front elevation view of a first embodiment of a hand-held electronic game machine showing our new design;

FIG. 2 is a rear elevational view thereof;

FIG. 3 is a top plan view thereof;

FIG. 4 is a bottom plan view thereof;

FIG. 5 is a right side view thereof; and,

FIG. 6 is a left side view thereof. 

The ornamental design for a hand-held electronic game machine, as shown and described. 